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Picture Recognizability with Automata Based on Wang Tiles

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Book cover SOFSEM 2010: Theory and Practice of Computer Science (SOFSEM 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5901))

Abstract

We introduce a model of automaton for picture language recognition which is based on tiles and is called Wang automaton, since its description relies on the notation of Wang systems. Wang automata combine features of both online tessellation acceptors and 4-ways automata: as in online tessellation acceptors, computation assigns states to each picture position; as in 4-way automata, the input head visits the picture moving from one pixel to an adjacent one, according to some scanning strategy. We prove that Wang automata recognize the class REC, i.e. they are equivalent to tiling systems or online tessellation acceptors, and hence strictly more powerful than 4-way automata. We also consider a very natural notion of determinism for Wang automata, and study the resulting class, comparing it with other deterministic classes considered in the literature, like DREC and Snake-DREC.

This work has been supported by the MIUR PRIN projects “Mathematical aspects and emerging applications of automata and formal languages”, and “D-ASAP: Dependable Adaptable Software Architecture for Pervasive Computing”.

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Author information

Authors and Affiliations

  1. Dipartimento di Scienze dell’Informazione, Università degli Studi di Milano, Via Comelico 39/41, 20135, Milano, Italy

    Violetta Lonati

  2. IEIIT, Consiglio Nazionale delle Ricerche, Via Golgi 40, 20133, Milano, Italy

    Matteo Pradella

Authors
  1. Violetta Lonati
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  2. Matteo Pradella
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Editor information

Editors and Affiliations

  1. Department of Information and Computing Sciences, Utrecht University, Padualaan 14, 3584 CH, Utrecht, The Netherlands

    Jan van Leeuwen

  2. LaBRI, Universit Bordeaux, 351 cours de la Libration, 1F-33405, Talence Cedex, France

    Anca Muscholl

  3. Department of Computer Science & Applied Mathematics, Weizmann Institute, Faculty of Mathematics and Computer Science, 76100, Rehovot, Israel

    David Peleg

  4. Department of Software Engineering Faculty of Mathematics and Physics Malostranské nám, Charles University, 25 11800, Prague 1, Czech Republic

    Jaroslav Pokorný

  5. Software Engineering, Department of Computer Science, RWTH Aachen University, 3, Ahornstrae 55, D-52074, Aachen, Germany

    Bernhard Rumpe

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Lonati, V., Pradella, M. (2010). Picture Recognizability with Automata Based on Wang Tiles. In: van Leeuwen, J., Muscholl, A., Peleg, D., Pokorný, J., Rumpe, B. (eds) SOFSEM 2010: Theory and Practice of Computer Science. SOFSEM 2010. Lecture Notes in Computer Science, vol 5901. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11266-9_48

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  • DOI: https://doi.org/10.1007/978-3-642-11266-9_48

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-11265-2

  • Online ISBN: 978-3-642-11266-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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